A novel fractal model for effective thermal conductivity in granular porous media

Quantitative prediction of effective thermal conductivity in porous media is very important in various industrial applications and scientific researches. As the topology and geometry characteristics of pore-solid space is extremely complicated, an accurately theoretical calculation in porous media is still a great challenge. In this study, a novel theoretical model of effective thermal conductivity is derived in granular porous media originated from the Laplace's Equation with a new boundary condition. The proposed model considers the size of solid particles following the fractal distribution characteristics, which is expressed as a function of porosity, fractal dimension of solid particle, maximum particle radius, representative length, and thermal conductivity of both solid particle and pore phase. The predictions of proposed model show a good agreement with the existing models and various published experimental data, which validates its accuracy and reliability. The effect of different geometrical parameters for proposed model is analyzed and discussed. This novel proposed model of effective thermal conductivity may reveal a better insight for thermophysical mechanisms in granular porous media than conventional models.